Fuzzy Broad Model Predictive Control Based on Hybrid-driven and Gradient Optimization
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摘要: 模型预测控制(MPC)是广泛应用于各类工业过程的先进过程控制策略. 深度神经网络能够提升传统MPC性能, 但存在计算复杂度高和过拟合风险. 在MPC中采用常规粒子群优化(PSO)虽具备全局搜索能力, 却因计算消耗和初始解依赖等问题难以满足实时控制需求. 针对上述问题, 提出基于知识−数据驱动和梯度PSO的模糊宽度MPC. 首先, 采用区间二型模糊宽度学习系统构建预测模型, 增强非线性建模和不确定性处理能力. 其次, 在滚动优化过程中, 引入梯度下降与PSO的协同策略, 以确保快速收敛并提升全局搜索性能, 同时利用系统样本数据库和粒子档案数据库构建知识−数据驱动的代理模型以降低计算消耗. 最后, 设计操纵变量基线求解策略以提高控制输出的安全性和可靠性. 通过典型非线性系统和实际城市固废焚烧过程控制的仿真实验, 验证了所提方法的有效性.Abstract: Model predictive control (MPC) is an advanced process control strategy widely applied across various industrial processes. Although deep neural networks have been used to enhance traditional MPC performance, they often suffer from high computational complexity and the risk of overfitting. While the application of conventional particle swarm optimization (PSO) in MPC offers global search capabilities, it struggles to meet real-time control requirements due to excessive computational overhead and strong dependency on initial solutions. To address these challenges, this paper proposes a novel fuzzy broad model predictive control approach based on knowledge-data-driven and gradient-enhanced PSO. Firstly, an interval type-2 fuzzy broad learning system is employed to construct the predictive model, thereby enhancing nonlinear modeling and uncertainty handling capabilities. Secondly, during the rolling optimization process, a hybrid strategy combining gradient descent and PSO is introduced to ensure fast convergence while improving global search performance. In addition, a knowledge-data-driven surrogate model is built by leveraging the system sample database and particle archive database to significantly reduce computational consumption. Finally, a baseline solving strategy for manipulated variables is designed to improve the safety and reliability of control outputs. The effectiveness of the proposed method is verified through simulation experiments on typical nonlinear systems and actual municipal solid waste incineration process.
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图 4 数值仿真实验中预测模型的拟合曲线图
Fig. 4 Fitting curve diagram of the prediction model in the numerical simulation experiment
图 5 数值仿真实验中案例1的跟踪、误差与MV曲线
Fig. 5 Tracking, error and MV curves of case 1 in the numerical simulation experiment
图 6 数值仿真实验中案例1和案例2的KDD模型拟合曲线
Fig. 6 KDD model fitting curves of case 1 and case 2 in the numerical simulation experiment
图 7 数值仿真实验中案例1和案例2的目标函数下降曲线
Fig. 7 Objective function descent curves of case 1 and case 2 in the numerical simulation experiment
图 8 数值仿真实验中案例2的跟踪、误差与MV曲线
Fig. 8 Tracking, error and MV curves of case 2 in the numerical simulation experiment
图 10 MSWI过程预测模型拟合曲线对比
Fig. 10 Comparison of fitting curves of MSWI process prediction models
图 11 MSWI过程案例3的跟踪、误差与MV曲线
Fig. 11 Tracking, error and MV curves of case 3 in MSWI process
图 14 MSWI过程案例4的跟踪、误差与MV曲线
Fig. 14 Tracking, error and MV curves of case 4 in MSWI process
图 12 MSWI过程案例3与案例4的KDD模型的拟合曲线
Fig. 12 Fitting curves of KDD model of case 3 and case 4 in MSWI process
图 13 MSWI过程案例3与案例4的目标函数下降曲线
Fig. 13 Objective function descent curves of case 3 and case 4 in MSWI process
图 16 PSO和GPSO的收敛特性对比
Fig. 16 Comparison of convergence characteristics between PSO and GPSO
图 17 KDD-GPSO-FBMPC算法超参数分析曲线
Fig. 17 KDD-GPSO-FBMPC algorithm hyperparameter analysis curves
B1 操纵变量与被控变量的互相关图
B1 Cross-correlation plots between manipulated variable and controlled variable
表 1 文献中的系统知识和粒子分布知识对比
Table 1 Comparison of system knowledge and particle distribution knowledge in literature
文献 知识描述对象 知识来源 知识描述内容与应用领域 性能提升 [44] 非线性控制系统 控制系统的源域数据 知识用于构建基于FNN的知识驱动模型, 以补充数据驱动模型的网络结构; 污水处理过程最优控制 从知识驱动模型中提取结构知识, 以补充数据驱动模型的网络结构信息, 解决在线数据不足的问题 [45] 系统的历史操作信息 知识用于自适应初始化策略, 以动态预设KDD优化控制的参数, 提高对非线性系统变化的适应性; 污水处理过程最优控制 引入知识后, 算法能够更快地响应系统操作需求的变化, 提高了系统的动态优化能力和响应速度 [46] 控制系统的专家操作经验 知识包括多个操作模型和子控制器, 通过数据共享和知识驱动机制改善控制精度; 污水处理过程切换控制 引入知识后, 算法能够更有效地处理信息不足的问题, 提高了控制的准确性和系统的稳定性 [47] 专家经验和操作规则 知识用于指导控制器采取补救措施, 消除污泥膨胀;污水处理过程污泥膨胀的自愈控制 引入知识后, 算法能够及时准确地调节操作变量, 实现从污泥膨胀中的自我恢复与安全稳定运行 [48] 已学习的多任务自回归模型 从已建模的自回归模型中提取高炉过程的非线性动态; 工业高炉炼铁过程中的熔铁、质量指数的在线估计和控制 通过从已建模的自回归模型中提取知识, 提高新模型对数据波动的鲁棒性、提高模型的准确性和控制性能 [49] 专家经验、领域知识、操作知识 与工业实际过程数据结合, 设计混合智能高级反馈控制方法; 矿物加工操作中的磨矿回路控制 通过数据与知识结合可以很容易地构建出复杂的工业过程以及智能控制方法的设计 [40] PSO优化算法 多目标的全局最优粒子的当前和历史非支配解的分布信息 多目标粒子群优化算法中全局最优值的选择; 基准函数和锌电解优化问题 粒子分布知识的引入为多目标PSO算法在基准函数和锌电解优化问题上的性能进行了显著改进 [37] 精英粒子的当前和历史位置信息 基于FNN的知识提取方法、知识评估机制和知识重构策略; 软件项目调度、路径规划、污水工业过程 知识的引入提高了粒子的适应动态环境能力以及种群的搜索性能 [50] 不同任务间的最优粒子的当前和历史位置信息 不同任务之间决策空间维度; 不同情况下的知识转移问题、基准优化问题与污水处理工程 通过知识迁移可以并行解决多个优化问题, 利用任务之间的知识转移提高优化效率 [51] 目标空间和决策空间 在知识迁移中识别和度量不利于种群进化的知识; 特征选择、符号回归等基准优化问题 对不利于种群的知识进行处理, 在抑制负迁移和提高收敛性能方面作用显著 
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表 2 数值仿真实验中预测模型性能指标对比
Table 2 Comparison of performance indicators of the prediction models in the numerical simulation experiment
模型 数据集 RMSE MAE R2 IT2FBLS 训练集 $ 1.666\;8\times10^{-2} $ $ 1.094\;6\times10^{-2} $ $ 9.976\;5\times10^{-1} $ 验证集 $ 1.762\;3\times10^{-2} $ $ 1.156\;0\times10^{-2} $ $ 9.966\;0\times10^{-1} $ 测试集 $ 2.452\;1\times10^{-2} $ $ 1.256\;2\times10^{-2} $ $ 9.941\;8\times10^{-1} $ FBLS 训练集 $ 4.741\;8\times10^{-2} $ $ 2.943\;7\times10^{-2} $ $ 9.809\;8\times10^{-1} $ 验证集 $ 5.868\;7\times10^{-2} $ $ 3.335\;2\times10^{-2} $ $ 9.622\;8\times10^{-1} $ 测试集 $ 7.528\;9\times10^{-2} $ $ 3.931\;3\times10^{-2} $ $ 9.451\;4\times10^{-1} $ IT2FNN 训练集 $ 8.537\;3\times10^{-2} $ $ 4.145\;0\times10^{-2} $ $ 9.383\;5\times10^{-1} $ 验证集 $ 6.784\;8\times10^{-2} $ $ 3.320\;7\times10^{-2} $ $ 9.495\;9\times10^{-1} $ 测试集 $ 1.143\;2\times10^{-1} $ $ 5.070\;7\times10^{-2} $ $ 8.735\;2\times10^{-1} $ FNN 训练集 $ 9.015\;2\times10^{-2} $ $ 4.017\;9\times10^{-2} $ $ 9.312\;6\times10^{-1} $ 验证集 $ 6.940\;9\times10^{-2} $ $ 2.980\;5\times10^{-2} $ $ 9.472\;4\times10^{-1} $ 测试集 $ 1.097\;2\times10^{-1} $ $ 4.741\;6\times10^{-2} $ $ 8.834\;9\times10^{-1} $
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表 3 数值仿真实验中案例1和案例2的控制性能指标对比
Table 3 Comparison of control performance indicators of case 1 and case 2 in the numerical simulation experiment
案例 控制器 ITSE IAE Devmax 时间 (s) 案例1 PID 8.2000 × 10−33.6100 × 10−27.0000 × 10−16.1900 × 10−1GD-IT2FBLS-MPC 3.8000 × 10−33.1500 × 10−27.0000 × 10−14.8416 × 100KDD-GPSO-FBMPC 2.1000 × 10−32.6503 × 10−27.0000 × 10−11.3651 × 101案例2 PID 1.1800 × 10−23.8400 × 10−27.0000 × 10−11.3140 × 100GD-IT2FBLS-MPC 7.8000 × 10−32.7300 × 10−27.0000 × 10−19.5155 × 100KDD-GPSO-FBMPC 4.9000 × 10−32.2367 × 10−27.0000 × 10−12.7572 × 101
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表 4 MSWI过程预测模型指标对比
Table 4 Comparison of indicators of MSWI process prediction models
模型 数据集 RMSE MAE R2 IT2FBLS 训练集 3.2470 × 1002.5153 × 1009.7098 × 10−1验证集 3.2974 × 1002.5141 × 1009.7013 × 10−1测试集 3.4554 × 1002.5692 × 1009.6730 × 10−1FBLS 训练集 4.1178 × 1023.1869 × 1009.5333 × 10−1验证集 4.0783 × 1003.2040 × 1009.5431 × 10−1测试集 4.2255 × 1003.3709 × 1009.5111 × 10−1IT2FNN 训练集 4.6324 × 1003.5122 × 1009.4093 × 10−1验证集 4.6063 × 1003.4569 × 1009.4172 × 10−1测试集 4.8139 × 1003.6823 × 1009.3654 × 10−1FNN 训练集 5.9173 × 1004.8588 × 1009.0362 × 10−1验证集 5.7912 × 1004.7234 × 1009.0787 × 10−1测试集 5.9673 × 1004.8703 × 1009.0249 × 10−1
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表 5 MSWI过程案例3与案例4的性能指标对比
Table 5 Performance indicators comparison of case 3 and case 4 in MSWI process
案例 控制器 ITSE IAE Devmax 时间 (s) 案例3 BO-IT2FNNC 2.8575 × 10−23.2800 × 10−13.9205 × 1008.4221 × 101CETFNMC 2.7355 × 10−23.2389 × 10−11.7313 × 1004.4747 × 10−1ET-OLFNRC 2.3614 × 10−22.4989 × 10−11.7313 × 1004.5439 × 10−1AMPC 2.6500 × 10−22.4801 × 10−11.6234 × 1001.0777 × 101KDD-GPSO-FBMPC 1.7213 × 10−21.7063 × 10−11.5438 × 1003.4101 × 101案例4 BO-IT2FNNC 4.3274 × 1005.4350 × 10−19.9399 × 1002.7355 × 101CETFNMC 4.0002 × 1005.5863 × 10−19.8047 × 1001.5080 × 101ET-OLFNRC 4.0314 × 1005.5171 × 10−19.8612 × 1001.5170 × 101AMPC 3.1669 × 1005.4212 × 10−16.5438 × 1003.8423 × 101KDD-GPSO-FBMPC 2.3457 × 1004.3130 × 10−16.5438 × 1001.8524 × 102
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表 7 GPSO和PSO的收敛特性对比
Table 7 Comparison of convergence characteristics between GPSO and PSO
条件 $J_{\text{mean}}(t)$ $J_{\text{max}}(t)$ $J_{\text{min}}(t)$ 时间 (s) 实验a 50 s PSO ( 5.2533 $\pm$0.0321 ) × 10−45.2878 × 10−45.0412 × 10−4− GPSO ( 3.8422 $\pm$0.0212 ) × 10−44.0951 × 10−43.6325 × 10−4− 实验b $e=0.5$ PSO ( 3.1542 $\pm$0.0092 ) × 10−43.2423 × 10−43.0423 × 10−287 GPSO ( 3.1389 $\pm$0.0013 ) × 10−43.2254 × 10−43.0544 × 10−222
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表 6 消融实验的性能指标对比
Table 6 Comparison of performance indicators of ablation experiments
控制器 ITSE IAE Devmax 时间 (s) BTF KDD-GPSO-NNMPC 2.5915 × 10−23.7724 × 10−11.9193 × 1001.9933 × 10111 KDD-PSO-FBMPC 2.1640 × 10−22.9156 × 10−11.5438 × 1004.8757 × 10136 KDD-GD-FBMPC 3.0979 × 10−22.9064 × 10−11.5438 × 1004.2719 × 100− GPSO-FBMPC 1.3500 × 10−22.3275 × 10−11.6534 × 1004.8139 × 10213 KDD-GPSO-FBMPC-3 2.8987 × 10−22.5930 × 10−11.6607 × 1002.4587 × 101− KDD-GPSO-FBMPC-2 2.4870 × 10−22.3819 × 10−11.5438 × 1002.6560 × 101− KDD-GPSO-FBMPC 4.8272 × 10−31.7440 × 10−11.5438 × 1002.6893 × 1016
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